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This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen from the deck.

How many hands contain 4 jacks?

Respuesta :

Plasmataco
There are 52 cards in a deck. Because you already assume you have 4 jacks, there are no more jacks in the deck. Assuming suits count, this means you have 52-4 different possibilities for your last card, so 48 possibilities.

Using the combination formula, it is found that 48 hands contain 4 jacks.

The order in which the cards are chosen is not important, and they are chosen without replacement, thus, the combination formula is used to solve this question.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

A standard deck contains 52 cards, 4 of which are jacks. Thus, we want:

  • 4 jacks from a set of 4.
  • 1 other card from a set of 48.

Then

[tex]T = C_{4,4}C_{48,1} = \frac{4!}{4!(4-4)!}\frac{48!}{1!47!} = 48[/tex]

48 hands contain 4 jacks.

A similar problem is given at https://brainly.com/question/24233657

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